function int = compute_int(f_value,j)
gauss_weights = [0.1259391805448;0.1259391805448;0.1259391805448;
    0.1323941527885;0.1323941527885;0.1323941527885;0.225];
int = f_value' * gauss_weights;
int = 0.5*j*int;
end